If ln a, ln b, ln c are in AP and ln a – ln 2b, ln 2b – ln 3c, ln 3c – ln a are in AP then a : b : c is
- 1 : 2 : 3
- 7 : 7 : 4
- 9 : 9 : 4
- 4 : 4 : 9
The Correct Option is C
Solution and Explanation
Top Questions on Arithmetic Progression
- Suppose that the number of terms in an A.P. is \( 2k, k \in \mathbb{N} \). If the sum of all odd terms of the A.P. is 40, the sum of all even terms is 55, and the last term of the A.P. exceeds the first term by 27, then \( k \) is equal to:
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- The 20th term from the end of the progression \[ 20, 19, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, \ldots, -129 \frac{1}{4} \] is:
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- Assertion (A): The sum of the first fifteen terms of the AP $21, 18, 15, 12, \dots$ is zero.
Reason (R): The sum of the first $n$ terms of an AP with first term $a$ and common difference $d$ is given by: \[ S_n = \frac{n}{2} \left[ a + (n - 1) d \right]. \]- CBSE Class X - 2024
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- The sum of the first three terms of an AP is 30 and the sum of the last three terms is 36. If the first term is 9, then the number of terms is :
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- How many terms of the $A.P.$ $27, 24, 21, . . .$ must be taken so that their sum is 105? Which term of the A.P. is zero?
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Questions Asked in JEE Main exam
- The sum of all local minimum values of the function \( f(x) \) as defined below is:
\[ f(x) = \left\{ \begin{array}{ll} 1 - 2x & \text{if } x < -1 \\ \frac{1}{3}(7 + 2|x|) & \text{if } -1 \leq x \leq 2 \\ \frac{11}{18} (x-4)(x-5) & \text{if } x > 2 \end{array} \right. \]
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- Let \(\vec{a} = i + j + k\), \(\vec{b} = 2i + 2j + k\) and \(\vec{d} = \vec{a} \times \vec{b}\). If \(\vec{c}\) is a vector such that \(\vec{a} \cdot \vec{c} = |\vec{c}|\), \(\|\vec{c} - 2\vec{d}\| = 8\) and the angle between \(\vec{d}\) and \(\vec{c}\) is \(\frac{\pi}{4}\), then \(\left|10 - 3\vec{b} \cdot \vec{c} + |\vec{d}|\right|^2\) is equal to:
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- Three infinitely long wires with linear charge density \( \lambda \) are placed along the x-axis, y-axis and z-axis respectively. Which of the following denotes an equipotential surface?
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Electrolysis of 600 mL aqueous solution of NaCl for 5 min changes the pH of the solution to 12. The current in Amperes used for the given electrolysis is ….. (Nearest integer).
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Concepts Used:
Arithmetic Progression
Arithmetic Progression (AP) is a mathematical series in which the difference between any two subsequent numbers is a fixed value.
For example, the natural number sequence 1, 2, 3, 4, 5, 6,... is an AP because the difference between two consecutive terms (say 1 and 2) is equal to one (2 -1). Even when dealing with odd and even numbers, the common difference between two consecutive words will be equal to 2.
In simpler words, an arithmetic progression is a collection of integers where each term is resulted by adding a fixed number to the preceding term apart from the first term.
For eg:- 4,6,8,10,12,14,16
We can notice Arithmetic Progression in our day-to-day lives too, for eg:- the number of days in a week, stacking chairs, etc.
Read More: Sum of First N Terms of an AP